Optimal Periodic Transmission Power Schedules for Remote Estimation of ARMA Processes

We consider periodic sensor transmission power allocation with an average energy constraint. The sensor sends its Kalman filter-based state estimate to the remote estimator through an unreliable link. Dropout probabilities depend on the power level used. To encompass applications where the estimator needs to attend to multiple tasks, we allow for irregular sampling, following a periodic pattern. Using properties of an underlying Markov chain model, we derive an explicit expression for the estimation error covariance. The results are then used to study optimal sensor power scheduling which minimizes the average error covariance.